Sum 20 coin flips mod 3 and you can find the bias in the output. It’s hard with a small sample set, but you could do it. Sum 10k coin flips and it’s a different situation.
Eventually you fall through the noise floor for any reasonable sample size.
It's almost certainly less effort (though arguably also less fun) to write a valid state checker than it is to prove that N random cube operations will yield something that's within some tolerance of a uniform distribution across all legal cube states.
Sum 20 coin flips mod 3 and you can find the bias in the output. It’s hard with a small sample set, but you could do it. Sum 10k coin flips and it’s a different situation.
Eventually you fall through the noise floor for any reasonable sample size.